Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation

Figure 3

Validity of maximum principles for the discrete Nagumo equation (78) with and . If is small enough we can apply Theorem 9; see subplot (a). For we can get weaker bounds (83) by the application of Theorem 11, subplots (b) and (c). If is greater than our results cannot be applied; see subplot (d).

(a)

(b) (i.e., )

(c) (i.e., )

(d) (i.e., )